Abstract
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily accurate, provided that errors per physical component are smaller than a certain threshold and independent of the computer size. However, in current experiments, physical-resource limitations such as energy, volume, or available bandwidth induce error rates that typically grow as the computer grows. We analyse how error correction performs under such constraints and show that the amount of error correction can be optimized, leading to a maximum attainable computational accuracy. We find this maximum for generic situations where noise is scale dependent. By inverting the logic, we provide experimenters with a tool for finding the minimum resources required to run an algorithm with a given computational accuracy. When combined with a full-stack quantum computing model, this provides the basis for energetic estimates of future large-scale quantum computers.Received 17 December 2020Accepted 13 October 2021DOI:https://doi.org/10.1103/PRXQuantum.2.040335Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum error correctionQuantum information architectures & platformsInterdisciplinary PhysicsQuantum Information
Highlights
With the advent of small-scale quantum computing devices from companies such as IBM and the myriad of software and hardware quantum startups, the interest in building quantum computers is at an all-time high
It has to be replaced by our theory presented here in two generic situations: (1) if a technological bottleneck stops one from increasing the resources in proportion to the number of physical components in the quantum computer; or (2) if one wants to minimize the resources consumed by the quantum computer
Many quantum computing technologies currently exhibit physical gate errors that grow with the size and complexity of the quantum computer
Summary
With the advent of small-scale quantum computing devices from companies such as IBM and the myriad of software and hardware quantum startups, the interest in building quantum computers is at an all-time high. A constraint on the available bandwidth makes the qubit transition frequencies closer and closer as the computer size grows, causing more and more crosstalk between qubits when performing gates [1] These three typical examples lead to a scale-dependent noise. The standard theory of FTQC applies when noise does not grow with scale It has to be replaced by our theory presented here in two generic situations: (1) if a technological bottleneck stops one from increasing the resources (energy, volume, bandwidth, etc.) in proportion to the number of physical components (qubits, gates, etc.) in the quantum computer; or (2) if one wants to minimize the resources consumed by the quantum computer. We focus on three physically motivated situations where resource constraints such as energy, volume, or bandwidth lead to scale-dependent noise and examine the feasibility of FTQC in the limit of large quantum computers. This suggests the possibility of a detailed energetic analysis for a full-stack quantum computer—which, goes beyond the scope of this paper
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